Generally, exemptions apply for research in which the identities of the people involved are not revealed. This could include educational tests where the information recorded is not linked to an identifiable individual, or testing of medical information or samples where the donor remains anonymous.
Researchers can design their programs in a way that means IRB approval is not necessary. The most straightforward way to do this is to find a way of collecting data that does not require participants to give information that could identify them.
Both students and professors conducting academic research involving human subjects will generally have to apply to their IRB for approval before starting work. Precise requirements vary from place to place, but the IRB will usually need a full description of the proposed research, including background, study rationale, methodology and a description of the potential importance of the research to make its decision.